Adiabatic quantum algorithm for search engine ranking

TL;DR

This paper introduces an adiabatic quantum algorithm to generate a quantum state encoding the PageRank vector, enabling faster ranking computations and property testing of web graphs with potential quantum speedups.

Contribution

The paper presents a novel adiabatic quantum algorithm for quantum PageRank state preparation, demonstrating polylogarithmic scaling and applications in efficient distribution testing.

Findings

Quantum PageRank state can be prepared in polylogarithmic time.

Quantum speedup in estimating top-ranked entries of PageRank.

Quantum protocols require exponentially fewer measurements for distribution testing.

Abstract

We propose an adiabatic quantum algorithm for generating a quantum pure state encoding of the PageRank vector, the most widely used tool in ranking the relative importance of internet pages. We present extensive numerical simulations which provide evidence that this algorithm can prepare the quantum PageRank state in a time which, on average, scales polylogarithmically in the number of webpages. We argue that the main topological feature of the underlying web graph allowing for such a scaling is the out-degree distribution. The top ranked $\log(n)$ entries of the quantum PageRank state can then be estimated with a polynomial quantum speedup. Moreover, the quantum PageRank state can be used in "q-sampling" protocols for testing properties of distributions, which require exponentially fewer measurements than all classical schemes designed for the same task. This can be used to decide whether to run a classical update of the PageRank.